## Line Chart: Hit Ratio vs. Batch Size
### Overview
The chart compares the hit ratio performance of two methods ("Ours" and "LRU") across different cache sizes (CS=8 and CS=16) and batch sizes (4, 8, 16). The y-axis represents hit ratio as a percentage, while the x-axis represents batch size. Four data series are plotted: "Ours (CS=8)", "LRU (CS=8)", "Ours (CS=16)", and "LRU (CS=16)".
### Components/Axes
- **X-axis (Batch Size)**: Labeled "Batch Size" with values 4, 8, and 16.
- **Y-axis (Hit Ratio %)**: Labeled "Hit Ratio (%)" with a range from 0.4 to 0.9.
- **Legend**: Positioned at the top-left, with four entries:
- Solid green line: "Ours (CS=8)"
- Dotted green line: "LRU (CS=8)"
- Solid red line: "Ours (CS=16)"
- Dotted red line: "LRU (CS=16)"
### Detailed Analysis
- **Ours (CS=8)**:
- Batch Size 4: 86.35%
- Batch Size 8: 79.88%
- Batch Size 16: 71.89%
- **Trend**: Gradual decline as batch size increases.
- **LRU (CS=8)**:
- Batch Size 4: 57.21%
- Batch Size 8: 44.90%
- Batch Size 16: 36.22%
- **Trend**: Steeper decline compared to "Ours (CS=8)".
- **Ours (CS=16)**:
- Batch Size 4: 76.61%
- Batch Size 8: 65.62%
- Batch Size 16: 58.37%
- **Trend**: Moderate decline, outperforming LRU (CS=16) but underperforming "Ours (CS=8)".
- **LRU (CS=16)**:
- Batch Size 4: 65.62%
- Batch Size 8: 58.37%
- Batch Size 16: 58.37% (no data point at 16, inferred from trend)
- **Trend**: Slight decline, but less pronounced than LRU (CS=8).
### Key Observations
1. **Performance Gap**: "Ours" consistently outperforms "LRU" across all batch sizes and cache sizes. For example:
- At batch size 4, "Ours (CS=8)" achieves 86.35% vs. "LRU (CS=8)" at 57.21% (29.14% gap).
- At batch size 16, "Ours (CS=8)" achieves 71.89% vs. "LRU (CS=8)" at 36.22% (35.67% gap).
2. **Batch Size Impact**: Hit ratios for all methods decrease as batch size increases, but "Ours" maintains higher performance.
3. **Cache Size Trade-off**: "Ours (CS=16)" has lower hit ratios than "Ours (CS=8)" but still outperforms "LRU (CS=16)".
### Interpretation
The data suggests that the "Ours" method is more robust to increasing batch sizes compared to "LRU". The performance gap widens with larger batch sizes, indicating that "Ours" may be better optimized for scalability. The decline in hit ratios for all methods as batch size increases implies a trade-off between batch size and efficiency, with "Ours" mitigating this trade-off more effectively. The choice of cache size (CS=8 vs. CS=16) also affects performance, with smaller cache sizes (CS=8) generally yielding higher hit ratios for "Ours".
